Experienced mountain bike navigators often attach a small clip-on compass to their map board. For mountain biking, you're not trying to navigate to small terrain features where a top quality compass would be necessary. You just want to confirm the rough direction that a trail is heading, understand a trail junction when you arrive at it, or figure out which end of the parking lot the flag will be on. For that, you just need to know where north is.
This is the compass I use for more complex orienteering.
It has a fast settling needle, which is good when you're moving quickly and changing directions a lot. It doesn't have a declination adjustment since orienteering maps are oriented to Magnetic north at the top of the page. For adventure racing, this means I need to do a little math because government topo maps are oriented to True north. I'm not sure what to recommend if you'd like a general compass that works well for both functions. Most adventure racers have a compass with declination adjustment. Suunto probably has some good ones.
It would be great if some of your other friends want to give this a try! :)